Hello I can not tell you if it is compatible with your new webhosting service as you would need to contact them directly and ask them if they have all the requirements listed here.
Transfering your application though is not hard. You would simply backup the database and all files. You would then upload them to the new server and restore everything there. You would need to edit the config-inc.php file and place any new database connection info in there and edit the $PP_PATH variable to the new server path. After this you would be able to login but you are not gonna see images dont worry. Go to Admin => Global Options and change your server paths for data and uploads to that of the new server. Then after saving that go to Admin - Storage Options and make sure to rever t those settings to load the new paths.
That should have you up and running on the new server. If there is anything else we can do let me know.